Related papers: Quantum codes from affine variety codes and their …
A class of powerful $q$-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $q$-ary block codes that encode $k$…
In this paper, we give a constructive proof to show that if there exist a classical linear code C is a subset of F_q^n of dimension k and a classical linear code D is a subset of F_q^k^m of dimension s, where q is a power of a prime number…
One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the…
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for the code dimension, depending on the two classical codes…
This article presents new constructions of quantum error correcting Calderbank-Shor-Steane (CSS for short) codes. These codes are mainly obtained by Sloane's classical combinations of linear codes applied here to the case of self-orthogonal…
We construct fermionic conformal field theories (CFTs) whose spectra are characterized by quantum stabilizer codes. We exploit our construction to search for fermionic CFTs with supersymmetry by focusing on quantum stabilizer codes of the…
In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance [[8; 2; 5]]4+i).
Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical self-orthogonal rate-1/n F_4-linear and binary linear convolutional…
A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed…
Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. In this paper, we give two new constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes and…
In this paper, we examine algebraic geometric (AG) codes associated with curves generated by separated polynomials, and we create AG codes and quantum stabilizer codes from these curves by varying their parameters. Our research involves a…
Asymmetric quantum error-correcting codes (AQCs) may offer some advantage over their symmetric counterparts by providing better error-correction for the more frequent error types. The well-known CSS construction of $q$-ary AQCs is extended…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$. They…
We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in [12, Ex. 3.2]. Among the codes that we construct almost all have parameters as good as the best known…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
This work develops a geometric framework for constructing quantum error-correcting codes from weighted projective and orbifold structures, integrating algebraic geometry, divisor theory, and the CSS stabilizer formalism. Beginning with…
Recently, quantum error-correcting codes were proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit flip and phase flip errors. An example for a channel which…
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…